A police spokeswoman said they received a report after the man was spotted near Christchurch's Spencer Park on Sunday.
"We spoke about there being quite a few families and people at the beach given it was such a warm day. That was quite concerning. There was no phone service where she saw him so she had to head back to her car and call the police," Croxson said.
Police are asking anyone who may have information about the incident to call 105 quoting file number 210418/5795.
A warning post on Facebook generated more than 100 comments with one commenter saying they were warned about the man a few weeks ago.
"As we were a group of three with dogs, he didn't do it to us but could see he was naked after we started walking away from him. He had binoculars looking to see who was coming."
Another comment said: "Might be the same guy that got caught doing it at pines a few weeks ago. He got chased down but got away."
A woman also reported seeing a man with a similar description, committing a similar act, on March 31.
"I took my daughter out for our morning hīkoi. We went to Spencer Park. As I was pushing my baby on the swing I noticed a caucasian 5"9 mid 30-40s aged man with a beer gut.
"He was of large build who had nothing but bright pink underwear on and black running shoes, no top and no pants. My daughter pointed to something and as I turned around I seen that he was fully exposed. I am beyond speechless and disgusted." the woman said in a Facebook post.